Consensus of Second-Order Multi-Agent Systems with Time-Varying Delays and Antagonistic Interactions

This study investigates the consensus problem of second-order multi-agent systems subject to time-varying interval-like delays. The notion of consensus is extended to networks containing antagonistic interactions modeled by negative weights on the communication graph. A unified framework is established to address both the stationary and dynamic consensus issues in sampled-data settings. Using the reciprocally convex approach, a sufficient condition for consensus is derived in terms of matrix inequalities. Numerical examples are provided to illustrate the effectiveness of the proposed result.